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!)
 A033455 Convolution of nonzero squares A000290 with themselves. 13
 1, 8, 34, 104, 259, 560, 1092, 1968, 3333, 5368, 8294, 12376, 17927, 25312, 34952, 47328, 62985, 82536, 106666, 136136, 171787, 214544, 265420, 325520, 396045, 478296, 573678, 683704, 809999, 954304, 1118480, 1304512, 1514513, 1750728, 2015538, 2311464 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Total area of all square regions from an n X n grid. E.g., at n = 3, there are nine individual squares, four 2 X 2's and one 3 X 3, total area 9 + 16 + 9 = 34, hence a(3) = 34. - Jon Perry, Jul 29 2003 If X is an n-set and Y and Z disjoint 2-subsets of X then a(n) is equal to the number of 7-subsets of X intersecting both Y and Z. - Milan Janjic, Aug 26 2007 Every fourth term is odd. However, there are no primes in the sequence. - Zak Seidov, Feb 28 2011 -120*a(n) is the real part of (n + n*i)*(n + 2 + n*i)*(n + (n + 2)i)*(n + 2+(n + 2)*i)*(n + 1 + (n + 1)*i), where i = sqrt(-1). - Jon Perry, Feb 05 2014 The previous formula rephrases the factorization of the 5th order polynomial a(n) = (n+1)*((n+1)^4-1) = (n+1)*A123864(n+1) based on the factorization in A123865. - R. J. Mathar, Feb 08 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Abderrahim Arabi, Hacène Belbachir, Jean-Philippe Dubernard, Plateau Polycubes and Lateral Area, arXiv:1811.05707 [math.CO], 2018. See Column 1 Table 1 p. 8. Milan Janjic, Two Enumerative Functions Milan Janjić, On Restricted Ternary Words and Insets, arXiv:1905.04465 [math.CO], 2019. C. P. Neuman and D. I. Schonbach, Evaluation of sums of convolved powers using Bernoulli numbers, SIAM Rev. 19 (1977), no. 1, 90--99. MR0428678 (55 #1698). See Table 2. - N. J. A. Sloane, Mar 23 2014 Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA a(n-1) = n*(n^4 - 1)/30 = A061167(n)/30. - Henry Bottomley, Apr 18 2001 G.f.: x*(1+x)^2/(1-x)^6. - Philippe Deléham, Feb 21 2012 a(n) = Sum_{k=1..n+1} k^2*(n+1-k)^2. - Kolosov Petro, Feb 07 2019 E.g.f.: x*(30 +90*x +65*x^2 +15*x^3 +x^4)*exp(x)/30. - G. C. Greubel, Jul 05 2019 MATHEMATICA Table[(n^5 - n)/30, {n, 2, 41}] (* Vladimir Joseph Stephan Orlovsky, Feb 28 2011 *) CoefficientList[Series[(1+x)^2/(1-x)^6, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 24 2014 *) PROG (MAGMA) [(n^5-n)/30: n in [2..41]]; // Vincenzo Librandi, Mar 24 2014 (PARI) vector(40, n, ((n+1)^5 -n-1)/30) \\ G. C. Greubel, Jul 05 2019 (Sage) [((n+1)^5 -n-1)/30 for n in (1..40)] # G. C. Greubel, Jul 05 2019 (GAP) List([1..40], n-> ((n+1)^5 -(n+1))/30) # G. C. Greubel, Jul 05 2019 CROSSREFS Cf. A000290, A001249, A123865, A219086. Sequence in context: A208639 A240785 A066804 * A172202 A053298 A196311 Adjacent sequences:  A033452 A033453 A033454 * A033456 A033457 A033458 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Vincenzo Librandi, Mar 24 2014 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 September 20 07:21 EDT 2020. Contains 337264 sequences. (Running on oeis4.)