A131874 a(n) = (7*n^2 + 15*n + 2) / 2.

1, 12, 30, 55, 87, 126, 172, 225, 285, 352, 426, 507, 595, 690, 792, 901, 1017, 1140, 1270, 1407, 1551, 1702, 1860, 2025, 2197, 2376, 2562, 2755, 2955, 3162, 3376, 3597, 3825, 4060, 4302, 4551, 4807, 5070, 5340, 5617, 5901, 6192, 6490, 6795, 7107, 7426

Offset

0,2

Comments

Row sums of triangle A131873.

Links

Table of n, a(n) for n=0..45.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

Binomial transform of (1, 11, 7, 0, 0, 0, ...).

a(n) = a(n-1) + 7*n + 4, (with a(0)=1). - Vincenzo Librandi, Nov 23 2010

a(n) = (2 + 15*n + 7*n^2)/2;

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3);

G.f.: (1 + 9*x - 3*x^2)/ (1-x)^3. - Colin Barker, Sep 13 2012

Example

a(2) = 30 = sum of row 2 terms of triangle A131873: (15 + 8 + 7).
a(2) = 30 = (1, 2, 1) dot (1, 11, 7) = (1 + 22 + 7).

Maple

A131874:=n->(2+15*n+7*n^2)/2; seq(A131874(n), n=0..100); # Wesley Ivan Hurt, Mar 26 2014

Prog

(PARI) a(n)=(7*n^2+15*n+2)/2 \\ Charles R Greathouse IV, Jun 16 2017

Crossrefs

Cf. A131873.

Sequence in context: A019557 A173107 A277978 * A111396 A080385 A120090

Adjacent sequences: A131871 A131872 A131873 * A131875 A131876 A131877

Keyword

nonn,easy

Author

Gary W. Adamson, Jul 22 2007

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Dec 04 2008

Status

approved