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

Author

Reinhard Zumkeller, Nov 23 2011

Keywords

• nonn
• easy

Comments

a(n) = Sum_{k=1..n} A199332(n,k);

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).

Programs

Haskell

a199771  = sum . a199332_row

Mathematica

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

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

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