A341043 a(n) = 16*n^3 - 36*n^2 + 30*n - 9.

1, 35, 189, 559, 1241, 2331, 3925, 6119, 9009, 12691, 17261, 22815, 29449, 37259, 46341, 56791, 68705, 82179, 97309, 114191, 132921, 153595, 176309, 201159, 228241, 257651, 289485, 323839, 360809, 400491, 442981, 488375, 536769, 588259, 642941, 700911, 762265

Offset: 1

Author

David Z Crookes, Feb 03 2021

Keywords

• nonn
• easy
• changed

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.

Examples

			For n = 3 the solution is 173 + 8 + 8 = 189.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000384, A000578, A155883.

Programs

PARI

Vec(x*(9*x^3+55*x^2+31*x+1)/(x-1)^4 + O(x^38)) \\ Elmo R. Oliveira, Sep 01 2025

Formula

a(n) = 16*n^3 - 36*n^2 + 30*n - 9.

a(n) = A155883(n) + 2*A000578(n-1).

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)

Extensions

More terms from Elmo R. Oliveira, Sep 01 2025