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A286918 Total number of nodes summed over all lattice paths from (0,0) to (n,n) using steps {(k,0), (0,k) | 0<k<=4} which never go above the diagonal x=y. 2
1, 3, 21, 159, 1257, 10046, 81811, 674184, 5605141, 46920874, 394949193, 3339464105, 28343082002, 241324470723, 2060357315568, 17632454524499, 151211115930880, 1299121121946684, 11179500360964780, 96344672766997340, 831385476662968094, 7182777882757416692 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(n) ~ c * d^n / sqrt(n), where d = 8.84734830841870961487278801886633962039798... is the real root of the equation 4 + 4*d - 8*d^2 - 8*d^3 + d^4 = 0 and c = 0.43633259077568249345422000202799136319250347607927734138960545201547... - Vaclav Kotesovec, May 30 2017

MAPLE

b:= proc(x, y) option remember; `if`(y>x or y<0, 0,

      `if`(x=0, [1$2], add((p-> p+[0, p[1]])(

         b(x-j, y)+b(x, y-j)), j=1..4)))

    end:

a:= n-> b(n$2)[2]:

seq(a(n), n=0..25);

CROSSREFS

Cf. A175891.

Sequence in context: A026333 A205773 A192364 * A189508 A074570 A136781

Adjacent sequences:  A286915 A286916 A286917 * A286919 A286920 A286921

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 17 2017

STATUS

approved

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Last modified August 25 05:19 EDT 2019. Contains 326318 sequences. (Running on oeis4.)