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A213782 Principal diagonal of the convolution array A213781. 4
1, 7, 19, 41, 72, 118, 176, 254, 347, 465, 601, 767, 954, 1176, 1422, 1708, 2021, 2379, 2767, 3205, 3676, 4202, 4764, 5386, 6047, 6773, 7541, 8379, 9262, 10220, 11226, 12312, 13449, 14671, 15947, 17313, 18736, 20254, 21832, 23510, 25251, 27097, 29009, 31031 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

FORMULA

a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).

G.f.: x*(1+5*x+4*x^2-2*x^4) / ((1-x)^4*(1+x)^2). - Corrected by Colin Barker, Jan 31 2016

From Colin Barker, Jan 31 2016: (Start)

a(n) = (16*n^3+66*n^2+6*(-1)^n*n-34*n-3*(-1)^n+3)/48.

a(n) = (8*n^3+33*n^2-14*n)/24 for n even.

a(n) = (8*n^3+33*n^2-20*n+3)/24 for n odd.

(End)

MATHEMATICA

(See A213781.)

LinearRecurrence[{2, 1, -4, 1, 2, -1}, {1, 7, 19, 41, 72, 118}, 50] (* Harvey P. Dale, Oct 17 2016 *)

PROG

(PARI) Vec(x*(1+5*x+4*x^2-2*x^4)/((1-x)^4*(1+x)^2) + O(x^100)) \\ Colin Barker, Jan 31 2016

CROSSREFS

Cf. A213781, A213500.

Sequence in context: A087762 A195349 A160422 * A269428 A097240 A097241

Adjacent sequences:  A213779 A213780 A213781 * A213783 A213784 A213785

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 22 2012

STATUS

approved

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Last modified November 21 14:18 EST 2019. Contains 329371 sequences. (Running on oeis4.)