A102296 a(n) = (1/6)*(n+1)*(10*n^2 + 17*n + 12).

2, 13, 43, 102, 200, 347, 553, 828, 1182, 1625, 2167, 2818, 3588, 4487, 5525, 6712, 8058, 9573, 11267, 13150, 15232, 17523, 20033, 22772, 25750, 28977, 32463, 36218, 40252, 44575, 49197, 54128, 59378, 64957, 70875, 77142, 83768, 90763, 98137

Offset: 0

Author

Creighton Dement, Feb 19 2005

Keywords

• easy
• nonn

Comments

A floretion-generated sequence which arises from a particular transform of the centered square numbers: A001844. Specifically, (a(n)) is the jesfor-transform of the sequence A001844 with respect to the floretion given in the program code. The sequence relates centered square numbers, triangular numbers and centered octahedral numbers to (n+1)^3. Note: this was made possible in part by the formula already given for A085786.

Floretion Algebra Multiplication Program, FAMP Code: 4jesforseq[ + .25'j + .25'k + .25j' + .25k' + .25'ij' + .25'ik' + .25'ji' + .25'ki' + e ], vesforseq = A001844, ForType: 1A, LoopType: tes.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A001844, A001845, A085786, A000217.

Programs

Magma

[(1/6)*(n+1)*(10*n^2+17*n+12): n in [0..50]]; // Vincenzo Librandi, May 30 2011

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {2, 13, 43, 102}, 50] (* Paolo Xausa, Mar 09 2024 *)

PARI

a(n) = (n+1)*(10*n^2+17*n+12)/6

Formula

G.f.: (x+1)*(3x+2)/(x-1)^4;

a(n) = 2*A001844(n+1)A001845(n+1)_0%20+%20A085786(n+1)_1%20(%20%22">0 - 2*A001845(n+1)_0 + A085786(n+1)_1 ( "" denotes offset ) (n+1)^3 = 2*A001845(n+1) - 2*A001844(n+1) - A000217(n+1) - a(n).