A277411 Column 1 of triangle A277410.

0, 3, 13, 38, 94, 213, 459, 960, 1972, 4007, 8089, 16266, 32634, 65385, 130903, 261956, 524080, 1048347, 2096901, 4194030, 8388310, 16776893, 33554083, 67108488, 134217324, 268435023, 536870449, 1073741330, 2147483122, 4294966737, 8589933999, 17179868556, 34359737704, 68719476035, 137438952733, 274877906166, 549755813070, 1099511626917, 2199023254651, 4398046510160

Offset: 1

Author

Paul D. Hanna, Oct 25 2016

Keywords

• nonn

Crossrefs

Cf. A277410, A277412.

Programs

PARI

{A277410(n, k) = my(A=x); for(i=1, n, A = x + subst(intformal(A +x*O(x^n)), x, y*A + (1-y)*x ) ); n!*polcoeff(polcoeff(A, n, x), k, y)}
for(n=1, 30, print1(A277410(n+1, 1), ", "));

Formula

Conjectures from Colin Barker, Nov 04 2016: (Start)

G.f.: x^2*(3-2*x) / ((1-x)^3*(1-2*x)).

a(n) = 5*a(n-1)-9*a(n-2)+7*a(n-3)-2*a(n-4) for n>4.

a(n) = (8*(2^n-1)-n*(n+7))/2. (End)