A061349 Sum of antidiagonals of A060736.

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

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) = a(n-1) + A001844(n-1) - A002378(A004526(n-1)).

a(n) = a(n-1) + n^2 + (n - 1)^2 - floor((n-1)/2)*floor((n+1)/2).

If n is odd then a(n) = (7*n^3 + 5*n)/12;

If n is even then a(n) = (7*n^3 + 8*n)/12.

From Colin Barker, Sep 13 2014: (Start)

a(n) = (n*(13 + 3*(-1)^n + 14*n^2))/24.

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*(x^4 + 4*x^3 + 4*x^2 + 4*x + 1)/((x - 1)^4*(x + 1)^2). (End)

E.g.f.: x*((12 + 21*x + 7*x^2)*cosh(x) + (15 + 21*x + 7*x^2)*sinh(x))/12. - Stefano Spezia, Jun 05 2023

Mathematica

LinearRecurrence[{2, 1, -4, 1, 2, -1}, {0, 1, 6, 17, 40, 75}, 50] (* Harvey P. Dale, Oct 17 2021 *)
Accumulate[Table[n^2 + (n - 1)^2 - Floor[((n-1)/2)]*Floor[((n+1)/2)], {n, 41}]] (* Stefano Spezia, Jun 05 2023 *)

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

Cf. A001844, A002378, A004526, A005900, A006918, A060736.

Sequence in context: A085278 A366104 A080275 * A213780 A101945 A220407

Adjacent sequences: A061346 A061347 A061348 * A061350 A061351 A061352

Keyword

nonn,easy

Author

Henry Bottomley, Jun 07 2001

Status

approved