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A095796 1 + (26*n+17+7*n^2)*n/2. 1
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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

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Last modified June 22 17:18 EDT 2021. Contains 345388 sequences. (Running on oeis4.)