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A174655 Partial sums of A049486. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..41.

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

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

EXAMPLE

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

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 *)

CROSSREFS

Cf. A049486, A049487.

Sequence in context: A065780 A220480 A105720 * A184631 A011933 A093802

Adjacent sequences:  A174652 A174653 A174654 * A174656 A174657 A174658

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Mar 25 2010

STATUS

approved

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Last modified June 21 00:16 EDT 2021. Contains 345324 sequences. (Running on oeis4.)