

A033455


Convolution of nonzero squares A000290 with themselves.


12



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
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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 nset and Y and Z disjoint 2subsets of X then a(n) is equal to the number of 7subsets 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)^41) = (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, JeanPhilippe Dubernard, Plateau Polycubes and Lateral Area, arXiv:1811.05707 [math.CO], 2018. See Column 1 Table 1 p. 8.
Milan Janjic, Two Enumerative Functions
C. P. Neuman and D. I. Schonbach, Evaluation of sums of convolved powers using Bernoulli numbers, SIAM Rev. 19 (1977), no. 1, 9099. 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(n1) = n*(n^41)/30 = A061167(n)/30.  Henry Bottomley, Apr 18 2001
G.f.: x*(1+x)^2/(1x)^6.  Philippe Deléham, Feb 21 2012


MATHEMATICA

Table[(n^5  n)/30, {n, 2, 60}] (* 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^5n)/30: n in [2..40]]; // Vincenzo Librandi, Mar 24 2014


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

N. J. A. Sloane


EXTENSIONS

More terms from Vincenzo Librandi, Mar 24 2014


STATUS

approved



