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A213826 Principal diagonal of the convolution array A213825. 4
2, 34, 132, 332, 670, 1182, 1904, 2872, 4122, 5690, 7612, 9924, 12662, 15862, 19560, 23792, 28594, 34002, 40052, 46780, 54222, 62414, 71392, 81192, 91850, 103402, 115884, 129332, 143782, 159270, 175832, 193504, 212322, 232322, 253540, 276012, 299774 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

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

FORMULA

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

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

G.f.: f(x)/g(x), where f(x) = 2*x*(1 + 13*x + 4*x^2) and g(x) = (1-x)^4.

a(n) = 2*A024215(n).

E.g.f.: (2 + 32*x + 33*x^2 + 6*x^3)*exp(x). - Franck Maminirina Ramaharo, Nov 23 2018

MATHEMATICA

(See A213825.)

CoefficientList[Series[2 (1 + 13 x + 4 x^2) / (1 - x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Nov 23 2018 *)

PROG

(MAGMA) [6*n^3-3*n^2-n: n in [1..40]]; // Vincenzo Librandi, Nov 23 2018

CROSSREFS

Cf. A213825.

Sequence in context: A200166 A226407 A226336 * A259108 A064202 A206624

Adjacent sequences:  A213823 A213824 A213825 * A213827 A213828 A213829

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jul 04 2012

STATUS

approved

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Last modified May 17 00:16 EDT 2021. Contains 343957 sequences. (Running on oeis4.)