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 A112610 Number of representations of n as a sum of two squares and two triangular numbers. 15
 1, 6, 13, 14, 18, 32, 31, 30, 48, 38, 42, 78, 57, 54, 80, 62, 84, 96, 74, 96, 121, 108, 90, 128, 98, 102, 192, 110, 114, 182, 133, 156, 176, 160, 138, 192, 180, 150, 234, 158, 192, 288, 183, 174, 240, 182, 228, 320, 194, 198, 272, 252, 240, 288, 256, 252, 403, 230 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also row sums of A239931, hence the sequence has a symmetric representation. - Omar E. Pol, Aug 30 2015 LINKS M. D. Hirschhorn, The number of representations of a number by various forms, Discrete Mathematics 298 (2005), 205-211. FORMULA a(n) = sigma(4n+1) where sigma(n) = A000203(n) is the sum of the divisors of n. Euler transform of period 4 sequence [ 6, -8, 6, -4, ...]. - Michael Somos, Jul 04 2006 Expansion of q^(-1/4)eta^14(q^2)/(eta^6(q)eta^4(q^4)) in powers of q. - Michael Somos, Jul 04 2006 Expansion of psi(q)^2*phi(q)^2, i.e., convolution of A004018 and A008441 [Hirschhorn]. - R. J. Mathar, Mar 24 2011 EXAMPLE a(1) = 6 since we can write 1 = 1^2 + 0^2 + 0 + 0 = (-1)^2 + 0^2 + 0 + 0 = 0^2 + 1^2 + 0 + 0 = 0^2 + (-1)^2 + 0 + 0 = 0^2 + 0^2 + 1 + 0 = 0^2 + 0^2 + 0 + 1 MATHEMATICA Table[DivisorSigma[1, 4 n + 1], {n, 0, 57}] (* Michael De Vlieger, Aug 31 2015 *) PROG (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^14/eta(x+A)^6/eta(x^4+A)^4, n))} /* Michael Somos, Jul 04 2006 */ (MAGMA) [DivisorSigma(1, 4*n+1): n in [0..60]]; // Vincenzo Librandi, Sep 18 2015 CROSSREFS Cf. A000203, A193553, A239052, A239053, A239931. Sequence in context: A244535 A066826 A031113 * A100205 A140888 A053753 Adjacent sequences:  A112607 A112608 A112609 * A112611 A112612 A112613 KEYWORD nonn AUTHOR James A. Sellers, Dec 21 2005 STATUS approved

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