OFFSET
1,2
COMMENTS
The n-th term of A155883 (hexagonal bifrustum numbers) has a hexagonal pyramid of [n - 1] set on each of its two hexagonal faces.
The digital roots run recursively 1, 8, 9.
The sum of the first n consecutive terms is the square of the n-th hexagonal number.
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = 16*n^3 - 36*n^2 + 30*n - 9.
G.f.: x*(1 + 31*x + 55*x^2 + 9*x^3)/(1 - x)^4. - Stefano Spezia, Feb 04 2021
From Elmo R. Oliveira, Sep 01 2025: (Start)
E.g.f.: 9 + exp(x)*(-9 + 10*x + 12*x^2 + 16*x^3).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
EXAMPLE
For n = 3 the solution is 173 + 8 + 8 = 189.
MATHEMATICA
Table[16n^3-36n^2+30n-9, {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 35, 189, 559}, 40] (* Harvey P. Dale, Apr 08 2026 *)
PROG
(PARI) Vec(x*(9*x^3+55*x^2+31*x+1)/(x-1)^4 + O(x^38)) \\ Elmo R. Oliveira, Sep 01 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
David Z Crookes, Feb 03 2021
EXTENSIONS
More terms from Elmo R. Oliveira, Sep 01 2025
STATUS
approved
