A095796 1 + (26*n+17+7*n^2)*n/2.

1, 26, 98, 238, 467, 806, 1276, 1898, 2693, 3682, 4886, 6326, 8023, 9998, 12272, 14866, 17801, 21098, 24778, 28862, 33371, 38326, 43748, 49658, 56077, 63026, 70526, 78598, 87263, 96542, 106456

Offset

0,2

Comments

Multiply the n-th power of the 4 X 4 matrix [1 0 0 0 / 1 1 0 0 / 2 3 1 0 / 6 12 7 1] by the column vector [1 1 1 1] from the right. Then a(n) is the last component of the vector that results, and A095794(n) the penultimate component.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4).

G.f. ( 1+22*x-2*x^3 ) / (x-1)^4 . - R. J. Mathar, Nov 05 2011

Example

806 = a(5) since M65 * [1 1 1 1] = [1 6 56 806] where 56 = A095794(5).

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {1, 26, 98, 238}, 40] (* Vincenzo Librandi, Jun 24 2012 *)
Table[1+(26n+17+7n^2)n/2, {n, 0, 30}] (* or *) CoefficientList[Series[ (1+ 22x- 2x^3)/(-1+x)^4, {x, 0, 30}], x]

Prog

(Magma) I:=[1, 26, 98, 238]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 24 2012

Crossrefs

Cf. A095794.

Sequence in context: A259291 A038654 A010014 * A256645 A175549 A159541

Adjacent sequences: A095793 A095794 A095795 * A095797 A095798 A095799

Keyword

nonn,easy

Author

Gary W. Adamson, Jun 06 2004

Status

approved