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A037235 a(n) = n*(2*n^2 - 3*n + 4)/3. 5

%I #42 Oct 21 2022 18:33:50

%S 0,1,4,13,32,65,116,189,288,417,580,781,1024,1313,1652,2045,2496,3009,

%T 3588,4237,4960,5761,6644,7613,8672,9825,11076,12429,13888,15457,

%U 17140,18941,20864,22913,25092,27405,29856,32449,35188,38077,41120,44321,47684,51213

%N a(n) = n*(2*n^2 - 3*n + 4)/3.

%C Row sums of triangle A134249. Also, binomial transform of (1, 3, 6, 4, 0, 0, 0, ...). - _Gary W. Adamson_, Oct 15 2007

%C Binomial transform of a(n) starts: 0, 1, 6, 28, 112, 400, 1312, 4032, ... . - _Wesley Ivan Hurt_, Oct 21 2014

%C Number of equivalence classes of n-tuples from the set {1,0,-1} where at the number of nonzero elements is 1,2, or 3 and two n-tuples are equivalent if they are negatives of each other. - _Michael Somos_, Oct 19 2022

%H Vincenzo Librandi, <a href="/A037235/b037235.txt">Table of n, a(n) for n = 0..1000</a>

%H T. A. Gulliver, <a href="http://web.archive.org/web/20070218033906/http://www.ece.uvic.ca/~agullive/square.ps">Sequences from Arrays of Integers</a>, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F G.f.: x*(1+3*x^2)/(1-x)^4.

%F a(n) = Sum_{k=0..n-1} (2*k^2 + 1). - _Mike Warburton_, Sep 08 2007

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) with n>3, a(0)=0, a(1)=1, a(2)=4, a(3)=13. - _Yosu Yurramendi_, Sep 03 2013

%F a(n+1) = a(n) + A058331(n). - _Michael Somos_, Oct 19 2022

%p A037235:=n->n*(2*n^2-3*n+4)/3: seq(A037235(n), n=0..50); # _Wesley Ivan Hurt_, Oct 21 2014

%t Table[n (2 n^2 - 3 n + 4)/3, {n, 0, 50}] (* _Wesley Ivan Hurt_, Oct 21 2014 *)

%o (PARI) A037235(n) = n*(2*n^2-3*n+4)/3 \\ _Michael B. Porter_, Dec 07 2009

%o (Magma) [n*(2*n^2-3*n+4)/3: n in [0..40]]; // _Vincenzo Librandi_, Jun 15 2011

%o (R)

%o a <- c(0, 1, 4, 13)

%o for(n in (length(a)+1):30) a[n] <- 4*a[n-1] -6*a[n-2] +4*a[n-3] -a[n-4]

%o a

%o # _Yosu Yurramendi_, Sep 03 2013

%Y Cf. A058331, A134249.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)