The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A294159 Alternating row sums of triangle A291844. 3
 1, 1, 2, 6, 18, 55, 171, 538, 1708, 5461, 17560, 56728, 183973, 598597, 1953145, 6388376, 20939664, 68764283, 226192964, 745146462, 2458020664, 8118111977, 26841209903, 88835163150, 294284206183, 975699571009, 3237456793478, 10749922312752, 35718863630895, 118757413662397 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Gheorghe Coserea, Table of n, a(n) for n = 0..303 FORMULA G.f. y(x) satisfies: 0 = (x^3 + x^2 + 3*x - 1)*(y^2 - y) + x. Conjecture: D-finite with recurrence n*a(n) +(-3*n+1)*a(n-1) +2*(-n+3)*a(n-2) +2*(n-5)*a(n-3) +(n-4)*a(n-4) +(n-5)*a(n-5)=0. - R. J. Mathar, Jun 17 2020 PROG (PARI) A291843_ser(N, t='t) = {   my(x='x+O('x^N), y=1, y1=0, n=1,   dn = 1/(-2*t^2*x^4 - (2*t^2+3*t)*x^3 - (2*t+1)*x^2 + (2*t-1)*x + 1));   while (n++,    y1 = (2*x^2*y'*((-t^2 + t)*x + (-t + 1) + (t^2*x^2 + (t^2 + t)*x + t)*y) +         (t*x^2 + t*x)*y^2 - (2*t^2*x^3 + 3*t*x^2 + (-t + 1)*x - 1))*dn;    if (y1 == y, break); y = y1; ); y; }; A291844_ser(N, t='t) = {   my(z = A291843_ser(N+1, t));   ((1+x)*z - 1)*(1 + t*x)/((1-t + t*(1+x)*z)*x*z^2); }; Vec(A291844_ser(30, -1)) \\ test: y=A291844_ser(200, -1); 0==(x^3 + x^2 + 3*x - 1)*(y^2 - y) + x CROSSREFS Cf. A291844. Sequence in context: A094590 A004529 A238236 * A000778 A006725 A066158 Adjacent sequences:  A294156 A294157 A294158 * A294160 A294161 A294162 KEYWORD nonn AUTHOR Gheorghe Coserea, Nov 03 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 11 03:09 EDT 2021. Contains 343784 sequences. (Running on oeis4.)