A356288 Sum of numbers in n-th upward diagonal of triangle the sum of {1; 2,3; 4,5,6; 7,8,9,10; ...} and {1; 2,3; 3,4,5; 4,5,6,7; ...}.

2, 4, 13, 20, 40, 55, 90, 116, 170, 210, 287, 344, 448, 525, 660, 760, 930, 1056, 1265, 1420, 1672, 1859, 2158, 2380, 2730, 2990, 3395, 3696, 4160, 4505, 5032, 5424, 6018, 6460, 7125, 7620, 8360, 8911, 9730, 10340, 11242, 11914, 12903, 13640, 14720, 15525, 16700

Offset

1,1

Links

Table of n, a(n) for n=1..47.

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

Formula

a(n) = (n * ceiling(n/2)) + ((15 + 25*n + 15*n^2 + 14*n^3 - 3*(((-1)^n))*(5 + n*(3 + n))) / 96).

a(n) = A079824(n) + A093005(n).

G.f.: x*(2 + 2*x + 3*x^2 + x^3 - x^4)/((1 - x)^4*(1 + x)^3). - Stefano Spezia, Aug 19 2022

Example

   2 = A079824(1) + A093005(1) =  1 + 1.
   4 = A079824(2) + A093005(2) =  2 + 2.
  13 = A079824(3) + A093005(3) =  7 + 6.
  20 = A079824(4) + A093005(4) = 12 + 8.

Prog

(Python)
def a(n): return (n * ((n + n % 2) // 2)) + (15 + 25*n + 15*(n**2) + 14*(n**3) - 3*(((-1)**n))*(5 + n*(3 + n))) // 96

Crossrefs

Cf. A079824, A093005.

Sequence in context: A018761 A276118 A179114 * A082015 A362263 A360397

Adjacent sequences: A356285 A356286 A356287 * A356289 A356290 A356291

Keyword

nonn,easy

Author

Torlach Rush, Aug 02 2022

Status

approved