A135966 - OEIS

A135966

Triangle, read by rows, where T(n,k) = fibonacci(k(n-k) + 1) for n>=k>=0.

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 5, 3, 1, 1, 5, 13, 13, 5, 1, 1, 8, 34, 55, 34, 8, 1, 1, 13, 89, 233, 233, 89, 13, 1, 1, 21, 233, 987, 1597, 987, 233, 21, 1, 1, 34, 610, 4181, 10946, 10946, 4181, 610, 34, 1, 1, 55, 1597, 17711, 75025, 121393, 75025, 17711, 1597, 55, 1

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OFFSET

0,8

LINKS

Table of n, a(n) for n=0..65.

FORMULA

T(n,k) = Sum_{j=0..k*(n-k)} binomial(j,k*(n-k)-j). - Seiichi Manyama, Jan 07 2026

EXAMPLE

Triangle begins:

1, 1;

1, 1, 1;

1, 2, 2, 1;

1, 3, 5, 3, 1;

1, 5, 13, 13, 5, 1;

1, 8, 34, 55, 34, 8, 1;

1, 13, 89, 233, 233, 89, 13, 1;

1, 21, 233, 987, 1597, 987, 233, 21, 1;

1, 34, 610, 4181, 10946, 10946, 4181, 610, 34, 1;

1, 55, 1597, 17711, 75025, 121393, 75025, 17711, 1597, 55, 1;

...

MATHEMATICA

Flatten[Table[Fibonacci[k(n-k)+1], {n, 0, 10}, {k, 0, n}]] (* Harvey P. Dale, Feb 03 2015 *)

PROG

(PARI) T(n, k)=fibonacci(k*(n-k)+1)

CROSSREFS

Columns k=0..7 give A000012, A000045, A122367, A033887, A033889, A099100, A134493, A134499.

Row sums give A135967.

Sequence in context: A034327 A034254 A157103 * A292741 A356802 A060351

Adjacent sequences: A135963 A135964 A135965 * A135967 A135968 A135969

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Dec 11 2007

STATUS

approved