A199771 Row sums of the triangle in A199332.

1, 5, 12, 26, 45, 75, 112, 164, 225, 305, 396, 510, 637, 791, 960, 1160, 1377, 1629, 1900, 2210, 2541, 2915, 3312, 3756, 4225, 4745, 5292, 5894, 6525, 7215, 7936, 8720, 9537, 10421, 11340, 12330, 13357, 14459, 15600, 16820, 18081, 19425, 20812, 22286, 23805

Offset

1,2

Comments

a(n) = sum(A199332(n,k): 1 <= k <= n);

a(2*n-1) = A015237(n); a(2*n) = A048395(n);

a(n+1) = A200252(n).

Links

Reinhard Zumkeller, 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

G.f. x*( 1+3*x+x^2+x^3 ) / ((1+x)^2*(x-1)^4). - R. J. Mathar, Nov 24 2011

a(n) = n*(3+2*n^2+4*n+(-1)^n))/8. - R. J. Mathar, Jun 23 2023

Mathematica

LinearRecurrence[{2, 1, -4, 1, 2, -1}, {1, 5, 12, 26, 45, 75}, 50] (* Harvey P. Dale, Apr 27 2019 *)

Prog

(Haskell)
a199771  = sum . a199332_row
(PARI) a(n)=([0, 1, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0; 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 1; -1, 2, 1, -4, 1, 2]^(n-1)*[1; 5; 12; 26; 45; 75])[1, 1] \\ Charles R Greathouse IV, Jun 18 2017

Crossrefs

Sequence in context: A294017 A367379 A212561 * A200252 A176448 A078517

Adjacent sequences: A199768 A199769 A199770 * A199772 A199773 A199774

Keyword

nonn,easy

Author

Reinhard Zumkeller, Nov 23 2011

Status

approved