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A154324 Diagonal sums of number triangle A113582. 1
1, 1, 2, 3, 6, 12, 23, 43, 74, 124, 195, 300, 441, 637, 890, 1226, 1647, 2187, 2848, 3673, 4664, 5874, 7305, 9021, 11024, 13390, 16121, 19306, 22947, 27147, 31908, 37348, 43469, 50405, 58158, 66879, 76570, 87400, 99371, 112671, 127302, 143472, 161183, 180664 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,0,-8,6,6,-8,0,3,-1).

FORMULA

G.f.: (1 -2*x -x^2 +5*x^3 -x^4 -2*x^5 +x^6)/((1-x)*(1-x^2))^3.

a(n) = Sum_{k=0..floor(n/2)} ( 1 + C(k+1,2)*C(n-2k+1,2) ).

From Colin Barker, Sep 12 2016: (Start)

a(n) = (2895 + 945*(-1)^n + (1786-90*(-1)^n)*n - 30*(3+(-1)^n)*n^2 + 40*n^3 + 30*n^4 + 4*n^5)/3840.

a(n) = (2*n^5+15*n^4+20*n^3-60*n^2+848*n+1920)/1920 for n even.

a(n) = (2*n^5+15*n^4+20*n^3-30*n^2+938*n+975)/1920 for n odd. (End)

MATHEMATICA

LinearRecurrence[{3, 0, -8, 6, 6, -8, 0, 3, -1}, {1, 1, 2, 3, 6, 12, 23, 43, 74}, 25] (* G. C. Greubel, Sep 11 2016 *)

CoefficientList[Series[(1 - 2 x - x^2 + 5 x^3 - x^4 - 2 x^5 + x^6) / ((1 - x) (1 - x^2))^3, {x, 0, 50}], x] (* Vincenzo Librandi, Sep 12 2016 *)

PROG

(PARI) Vec((1-2*x-x^2+5*x^3-x^4-2*x^5+x^6) / ((1-x)^6*(1+x)^3) + O(x^60)) \\ Colin Barker, Sep 12 2016

CROSSREFS

Sequence in context: A068012 A261930 A019138 * A001630 A164363 A103341

Adjacent sequences:  A154321 A154322 A154323 * A154325 A154326 A154327

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Jan 07 2009

STATUS

approved

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Last modified September 30 17:44 EDT 2016. Contains 276649 sequences.