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 A117403 a(n) = Sum_{k=0..[n/2]} 2^((n-2*k)*k) for n>=0. 2
 1, 1, 2, 3, 6, 13, 34, 105, 386, 1681, 8706, 53793, 395266, 3442753, 35659778, 440672385, 6476038146, 112812130561, 2336999211010, 57759810847233, 1697654543745026, 59146046307566593, 2450521284684021762 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Equals the antidiagonal sums of triangle A117401. LINKS FORMULA G.f.: A(x) = Sum_{n>=0} x^n / (1 - 2^n*x^2). a(2*n) = Sum_{k=0..n} 4^((n-k)*k); a(2*n+1) = Sum_{k=0..n} 2^k * 4^((n-k)*k). G.f.: 1/(1-x^2) - x/(Q(0) +x-x^3), where Q(k) = x^2*(2+x)*2^k -1-x - x*(2*x^2*2^k -1)^2/Q(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Nov 11 2013 EXAMPLE G.f.: A(x) = 1 + x + 2*x^2 + 3*x^3 + 6*x^4 + 13*x^5 + 34*x^6 + 105*x^7 +... where A(x) = 1/(1-x^2) + x/(1-2*x^2) + x^2/(1-4*x^2) + x^3/(1-8*x^2) + x^4/(1-16*x^2) + ... PROG (PARI) a(n)=sum(k=0, n\2, 2^((n-2*k)*k)) (PARI) {a(n)=polcoeff(sum(m=0, n, x^m/(1-2^m*x^2 +x*O(x^n))), n)} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A117401 (triangle), A117402 (row sums). Sequence in context: A202086 A227366 A171878 * A002877 A065845 A137273 Adjacent sequences:  A117400 A117401 A117402 * A117404 A117405 A117406 KEYWORD nonn AUTHOR Paul D. Hanna, Mar 12 2006 EXTENSIONS Name changed by Paul D. Hanna, Nov 11 2013 STATUS approved

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Last modified May 14 16:48 EDT 2021. Contains 343898 sequences. (Running on oeis4.)