The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A118187 Antidiagonal sums of triangle A118185: a(n) = Sum_{k=0..[n/2]} 4^(k*(n-2*k)) for n>=0. 3
 1, 1, 2, 5, 18, 81, 514, 5185, 73730, 1327361, 33685506, 1359217665, 77311508482, 5567355555841, 565149010231298, 91215553426898945, 20753150033413537794, 5977902509385249259521, 2427296516310194305630210 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..100 FORMULA G.f.: A(x) = Sum_{n>=0} x^n/(1-4^n*x^2). a(2*n) = Sum_{k=0..n} 4^(2*k*(n-k)). a(2*n+1) = Sum_{k=0..n} (4^k)^(2*(n-k)+1). EXAMPLE A(x) = 1/(1-x^2) + x/(1-4*x^2) + x^2/(1-16*x^2) + x^3/(1-64*x^2) + ...   = 1 + x + 2*x^2 + 5*x^3 + 18*x^4 + 81*x^5 + 514*x^6 + ... MATHEMATICA Table[Sum[4^(k*(n-2*k)), {k, 0, Floor[n/2]}], {n, 0, 30}] (* G. C. Greubel, Jun 29 2021 *) PROG (PARI) a(n)=sum(k=0, n\2, (4^k)^(n-2*k) ) (MAGMA) [(&+[4^(k*(n-2*k)): k in [0..Floor(n/2)]]): n in [0..30]]; // G. C. Greubel, Jun 29 2021 (Sage) [sum(4^(k*(n-2*k)) for k in (0..n//2)) for n in (0..30)] # G. C. Greubel, Jun 29 2021 CROSSREFS Cf. A118185 (triangle), A118186 (row sums). Sequence in context: A111916 A328440 A308634 * A307773 A332776 A038720 Adjacent sequences:  A118184 A118185 A118186 * A118188 A118189 A118190 KEYWORD nonn AUTHOR Paul D. Hanna, Apr 15 2006 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 January 28 03:20 EST 2022. Contains 350654 sequences. (Running on oeis4.)