A351704 Sums of the ascending diagonals of the triangle A162609.

1, 1, 2, 3, 7, 10, 20, 26, 45, 55, 86, 101, 147, 168, 232, 260, 345, 381, 490, 535, 671, 726, 892, 958, 1157, 1235, 1470, 1561, 1835, 1940, 2256, 2376, 2737, 2873, 3282, 3435, 3895, 4066, 4580, 4770, 5341, 5551, 6182, 6413, 7107, 7360, 8120, 8396, 9225, 9525, 10426, 10751, 11727, 12078, 13132, 13510, 14645

Offset: 0

Author

Eddie Gutierrez, May 05 2022

Keywords

• nonn

Comments

Each term is the sum of an ascending diagonal of the triangle A162609.

Examples

			a(4) = (64 + 8 + 12)/12 = 7
a(5) = (250 - 75 + 50 + 15)/24 = 10.
		

Links

• Eddie Gutierrez, The Wheel Octagon Triangle - Ascending Diagonals (Part VIIIb)

Crossrefs

Cf. A162609.

Programs

C

// Calculates and prints out the triangle and terms of ascending diagonals (on first line). To get more terms increment j.
#include 
int main()
{
   int n, j=8, k, C, F1, F2,s;
   F1=1; F2=1;
   printf("%d ", F1);
   printf("%d ", F2);
   for (s=0;s<=j;s++)
   {
      F1=F1 + 2*s*s + 2*s + 1;
      F2=F2 + 2*s*s + 3*s + 2;
      printf("%d ", F1);
      printf("%d ", F2);
   }
   printf("\n");
   return 0;
}

Formula

a(n) = (n^3 + 2*n + 12)/12, for even n.

a(n) = (2*n^3 - 3*n^2 + 10*n + 15)/24, for odd n.