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A159693 Partial sums of A000463. 2
1, 2, 4, 8, 11, 20, 24, 40, 45, 70, 76, 112, 119, 168, 176, 240, 249, 330, 340, 440, 451, 572, 584, 728, 741, 910, 924, 1120, 1135, 1360, 1376, 1632, 1649, 1938, 1956, 2280, 2299, 2660, 2680, 3080, 3101, 3542, 3564, 4048, 4071, 4600, 4624, 5200, 5225, 5850 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Sum of integers followed by squares.
LINKS
FORMULA
a(n) = (n^3+3*n^2+8*n+r(n))/24, where r(n) = 3*n+9 if n is odd, 3*n^2 if n is even.
G.f.: x*(1+x-x^2+x^3)/((1+x)^3*(x-1)^4). - R. J. Mathar, Apr 20 2009
a(n) = a(n-1)+3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7). - R. J. Mathar, Apr 20 2009
a(n) = (2*n^3+9*n^2+19*n+9+3*(n^2-n-3)*(-1)^n)/48. - Luce ETIENNE, Dec 29 2014
E.g.f.: (2*x^3+15*x^2+30*x+9)*exp(x)/48 +(x^2-3)*exp(-x)/16. - Robert Israel, Dec 30 2014
EXAMPLE
For n=9, a(n) = 1+1+2+4+3+9+4+16+5 = 45.
MAPLE
seq((2*n^3+9*n^2+19*n+9+3*(n^2-n-3)*(-1)^n)/48, n=1..100); # Robert Israel, Dec 30 2014
MATHEMATICA
CoefficientList[Series[x*(1+x-x^2+x^3)/((1+x)^3*(x-1)^4), {x, 0, 50}], x] (* or *) Table[(2*n^3+9*n^2+19*n+9+3*(n^2-n-3)*(-1)^n)/48, {n, 0, 50}] (* G. C. Greubel, Jun 02 2018 *)
Accumulate[Flatten[{#, #^2}&/@Range[30]]] (* Harvey P. Dale, Nov 30 2019 *)
PROG
(Magma) S:=&cat[ [ n, n^2 ]: n in [1..25] ]; [ n eq 1 select S[1] else Self(n-1)+S[n]: n in [1..#S] ]; // Klaus Brockhaus, Apr 20 2009
(Haskell)
a159693 n = a159693_list !! (n-1)
a159693_list = scanl1 (+) a000463_list -- Reinhard Zumkeller, Nov 08 2015
CROSSREFS
Sequence in context: A282620 A320440 A288149 * A363735 A053437 A018277
KEYWORD
nonn
AUTHOR
Gerald Hillier, Apr 20 2009
EXTENSIONS
More terms from R. J. Mathar and Klaus Brockhaus, Apr 20 2009
STATUS
approved

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Last modified December 2 01:36 EST 2023. Contains 367505 sequences. (Running on oeis4.)