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A061349 Sum of antidiagonals of A060736. 0
0, 1, 6, 17, 40, 75, 130, 203, 304, 429, 590, 781, 1016, 1287, 1610, 1975, 2400, 2873, 3414, 4009, 4680, 5411, 6226, 7107, 8080, 9125, 10270, 11493, 12824, 14239, 15770, 17391, 19136, 20977, 22950, 25025, 27240, 29563, 32034, 34619, 37360, 40221 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(1)=1, a(2)=2+4=6, a(3)=5+3+9=17, a(4)=10+6+8+16=40.

LINKS

Table of n, a(n) for n=0..41.

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

FORMULA

a(n) = A005900(n)-A006918(n) = a(n-1)+A001844(n-1)-A002378(A004526(n-1)) = a(n-1)+n^2+(n-1)^2-[(n-1)/2][(n+1)/2] with a(0)=0.

If n is odd then a(n)=(7n^3+5n)/12; if n is even then a(n)=(7n^3+8n)/12.

a(n) = (n*(13+3*(-1)^n+14*n^2))/24. - Colin Barker, Sep 13 2014

a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6). - Colin Barker, Sep 13 2014

G.f.: x*(x^4+4*x^3+4*x^2+4*x+1) / ((x-1)^4*(x+1)^2). - Colin Barker, Sep 13 2014

PROG

(PARI) concat(0, Vec(x*(x^4+4*x^3+4*x^2+4*x+1)/((x-1)^4*(x+1)^2) + O(x^100))) \\ Colin Barker, Sep 13 2014

CROSSREFS

Sequence in context: A004799 A085278 A080275 * A213780 A101945 A220407

Adjacent sequences:  A061346 A061347 A061348 * A061350 A061351 A061352

KEYWORD

nonn,easy

AUTHOR

Henry Bottomley, Jun 07 2001

STATUS

approved

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Last modified July 30 07:18 EDT 2021. Contains 346348 sequences. (Running on oeis4.)