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 A036498 Numbers of the form m*(6*m-1) and m*(6*m+1), where m is an integer. 11
 0, 5, 7, 22, 26, 51, 57, 92, 100, 145, 155, 210, 222, 287, 301, 376, 392, 477, 495, 590, 610, 715, 737, 852, 876, 1001, 1027, 1162, 1190, 1335, 1365, 1520, 1552, 1717, 1751, 1926, 1962, 2147, 2185, 2380, 2420, 2625, 2667, 2882, 2926, 3151, 3197, 3432, 3480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS PartitionQ[ p ] is odd and contains an extra even partition; series term z^p in Product( 1-z^n, (n,1,oo) ) has coefficient (+1). - Wouter Meeussen Numbers n such that the number of partitions of n into distinct parts with an even number of parts exceed by 1 the number of partitions of n into distinct parts with an odd number of parts. [See, e.g., the Freitag-Busam reference given under A036499, p. 410. - Wolfdieter Lang, Jan 18 2016] In formal power series, A010815=(product(1-x^k),k>0), ranks of coefficients 1 (A001318=ranks of nonzero (1 or -1) in A010815=ranks of odds terms in A000009). LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1). FORMULA a(n) = n(n+1)/6 for n=0 or 5 (mod 6). a(n) = 1/8*(-1+(-1)^n+2*n)*(-3+(-1)^n+6*n) (see MATHEMATICA code). G.f.: x^2*(5+2*x+5*x^2)/((1+x)^2*(1-x)^3). - Colin Barker, Apr 02 2012 a(1)=0, a(2)=5, a(3)=7, a(4)=22, a(5)=26, a(n)=a(n-1)+2*a(n-2)- 2*a(n-3)- a(n-4)+a(n-5). - Harvey P. Dale, Aug 13 2012 Bisections: a(2*k+1) = A001318(4*k) = k*(1+6*k) = A049453(k), k >= 0; a(2*k) = A001318(4*k-1) = k*(-1+6*k) = A049452(k), k >= 1. - Wolfdieter Lang, Jan 18 2016 MAPLE p1 := n->n*(6*n-1): p2 := n->n*(6*n+1): S:={}: for n from 0 to 100 do S := S union {p1(n), p2(n)} od: S MATHEMATICA Table[ 1/8*(-1 + (-1)^k + 2*k)*(-3 + (-1)^k + 6*k), {k, 64} ] CoefficientList[Series[x*(5+2*x+5*x^2)/((1+x)^2*(1-x)^3), {x, 0, 50}], x] (* Vincenzo Librandi, Apr 24 2012 *) Rest[Flatten[{#(6#-1), #(6#+1)}&/@Range[0, 30]]] (* or *) LinearRecurrence[ {1, 2, -2, -1, 1}, {0, 5, 7, 22, 26}, 60] (* Harvey P. Dale, Aug 13 2012 *) PROG (PARI) \ps 5000; for(n=1, 5000, if(polcoeff(eta(x), n, x)==1, print1(n, ", "))) (PARI) concat(0, Vec(x^2*(5+2*x+5*x^2)/((1+x)^2*(1-x)^3) + O(x^100))) \\ Altug Alkan, Jan 19 2016 (MAGMA) [1/8*(-1+(-1)^n+2*n)*(-3+(-1)^n+6*n): n in [1..50]]; // Vincenzo Librandi, Apr 24 2012 (MAGMA) /* By definition: */ A036498:=func; [0] cat [A036498(n*m): m in [-1, 1], n in [1..25]]; // Bruno Berselli, Nov 13 2012 CROSSREFS Cf. A000009, A001318, A010815, A036499. Union of A049452 and A049453. Sequence in context: A162462 A165144 A084164 * A248086 A076409 A294154 Adjacent sequences:  A036495 A036496 A036497 * A036499 A036500 A036501 KEYWORD nonn,easy AUTHOR EXTENSIONS Better description from Claude Lenormand (claude.lenormand(AT)free.fr), Feb 12 2001 Additional comments and more terms from James A. Sellers, Feb 14 2001 STATUS approved

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Last modified June 5 10:29 EDT 2020. Contains 334840 sequences. (Running on oeis4.)