A174655 Partial sums of A049486.

1, 5, 15, 36, 70, 123, 197, 298, 428, 593, 795, 1040, 1330, 1671, 2065, 2518, 3032, 3613, 4263, 4988, 5790, 6675, 7645, 8706, 9860, 11113, 12467, 13928, 15498, 17183, 18985, 20910, 22960, 25141, 27455, 29908, 32502, 35243, 38133, 41178, 44380

Offset: 1

Author

Jonathan Vos Post, Mar 25 2010

Keywords

• nonn

Comments

Partial sums of maximum length of non-crossing path on n X n square lattice. The subsequence of primes in this partial sum begins: 5, 197, 593, 3613, 11113, 17183.

Examples

			a(7) = 1 + 4 + 10 + 21 + 34 + 53 + 74 = 197 is prime.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (3, -2, -2, 3, -1).

Crossrefs

Cf. A049486, A049487.

Programs

Mathematica

Accumulate[Join[{1,4},LinearRecurrence[{2,0,-2,1},{10,21,34,53},40]]] (* or *) Join[{1,5},LinearRecurrence[{3,-2,-2,3,-1},{15,36,70,123,197},40]] (* Harvey P. Dale, Aug 21 2013 *)

Formula

a(n) = SUM[i=1..n] A049486(i).

Conjecture: a(n) = (3*(-9+(-1)^n)+34*n-12*n^2+8*n^3)/12 for n>1. G.f.: x*(x^5-x^4+3*x^3+2*x^2+2*x+1) / ((x-1)^4*(x+1)). - Colin Barker, May 02 2013