A176422 - OEIS

A176422

Triangle read by rows: T(n,k) = 1 + (q-binomial coefficient [n,k] for q=4) - binomial(n,k).

1, 1, 1, 1, 4, 1, 1, 19, 19, 1, 1, 82, 352, 82, 1, 1, 337, 5788, 5788, 337, 1, 1, 1360, 93079, 376786, 93079, 1360, 1, 1, 5455, 1490833, 24208579, 24208579, 1490833, 5455, 1, 1, 21838, 23859082, 1550842030, 6221613472, 1550842030, 23859082, 21838, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,5

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)

FORMULA

T(n,k) = A022168(n,k) - A007318(n,k) + 1.

EXAMPLE

Triangle begins:

1, 1;

1, 4, 1;

1, 19, 19, 1;

1, 82, 352, 82, 1;

1, 337, 5788, 5788, 337, 1;

1, 1360, 93079, 376786, 93079, 1360, 1;

1, 5455, 1490833, 24208579, 24208579, 1490833, 5455, 1;

1, 21838, 23859082, 1550842030, 6221613472, 1550842030, 23859082, 21838, 1;

...

MATHEMATICA

c[n_, q_] = Product[1 - q^i, {i, 1, n}];

t[n_, m_, q_] = c[n, q]/(c[m, q]*c[n - m, q]) - Binomial[n, m] + 1;

Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]

PROG

(PARI) T(n, q=4) = my(c=matpascal(n, q)-matpascal(n)); vector(n+1, n, vector(n, k, 1 + c[n, k]));

{ my(A=T(8)); for(i=1, #A, print(A[i])) } \\ Andrew Howroyd, Nov 18 2025

CROSSREFS

Cf. A007318, A022168, A176420, A176421.

Sequence in context: A323849 A254442 A340476 * A156586 A181544 A154283

Adjacent sequences: A176419 A176420 A176421 * A176423 A176424 A176425

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Apr 17 2010

EXTENSIONS

Edited by Andrew Howroyd, Nov 18 2025

STATUS

approved