A131878 a(n) = 7*n^2 + 14*n + 1.

1, 22, 57, 106, 169, 246, 337, 442, 561, 694, 841, 1002, 1177, 1366, 1569, 1786, 2017, 2262, 2521, 2794, 3081, 3382, 3697, 4026, 4369, 4726, 5097, 5482, 5881, 6294, 6721, 7162, 7617, 8086, 8569, 9066, 9577, 10102, 10641, 11194, 11761, 12342, 12937, 13546, 14169, 14806, 15457, 16122, 16801, 17494

Offset: 0

Author

Gary W. Adamson, Jul 22 2007

Keywords

• nonn
• easy

Comments

The original terms listed here were incorrect: 1002 through 8086 were listed as 988 through 8072, consistently 14 lower than the actual values. - Russ Cox, Apr 18 2024

Examples

			a(2) = 57 = sum of row 2 terms of triangle A131876: (29 + 15 + 13).
a(2) = 57 = (1, 2, 1) dot (1, 21, 14) = (1 + 42 + 14).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Takao Komatsu, Ritika Goel, and Neha Gupta, The Frobenius number for the triple of the 2-step star numbers, arXiv:2409.14788 [math.CO], 2024. See p. 2.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A131876.

Programs

Mathematica

Table[7n^2+14n+1,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{1,22,57},50] (* Harvey P. Dale, Mar 31 2025 *)

Formula

Binomial transform of (1, 21, 14, 0, 0, 0, ...).

a(n) = a(n-1) + 14*n + 7 (with a(0)=1). - Vincenzo Librandi, Nov 23 2010

Row sums of triangle A131876.

From Stefano Spezia, Sep 27 2024: (Start)

G.f.: (1 + 19*x - 6*x^2)/(1 - x)^3.

E.g.f.: exp(x)*(1 + 21*x + 7*x^2). (End)

Extensions

Corrected and extended by Russ Cox, Apr 18 2024