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A085789
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Partial sums of n 3-spaced triangular numbers beginning with t(2), e.g. a(2)=t(2)+t(5)=3+15=18.
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1
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3, 18, 54, 120, 225, 378, 588, 864, 1215, 1650, 2178, 2808, 3549, 4410, 5400, 6528, 7803, 9234, 10830, 12600, 14553, 16698, 19044, 21600, 24375, 27378, 30618, 34104, 37845, 41850, 46128, 50688, 55539, 60690, 66150, 71928, 78033, 84474, 91260, 98400, 105903
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Sums of rows of triangle A100345 (n>0).
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FORMULA
| 3/2 * n^2(n+1).
a(n) = 3*n*binomial(n+1,2) = 3*n*A000217(n) = 3*A002411(n). [Arkadiusz Wesolowski, Feb 10 2012]
G.f.: 3*(x + 2*x^2)/(1 - x)^4. [Arkadiusz Wesolowski, Feb 11 2012]
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MAPLE
| seq(add((n^2-k^2+(n+k)^2)/2, k=0..n), n=1..39); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 01 2006
a:=n->sum ((j+n+1)*n, j=1..n): seq(a(n), n=1..39); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 17 2006
restart: a:=n->sum(sum(k, j=3..n), k=0..n): seq(a(n), n=1..53):b:=n->sum(sum(n, j=0..n), k=0..n): seq(a(n), n=1..53):c:=b+a:seq(c(n), n=1..39); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 24 2008]
a:=n->add(binomial(n, 2)+add(n, j=2..n), j=2..n):seq(a(n), n=2..40); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 27 2008]
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MATHEMATICA
| Table[Sum[(n+i)*n, {i, 0, n}], {n, 1, 100}] (* From Vladimir Joseph Stephan Orlovsky, June 03 2011 *)
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PROG
| (PARI) v=vector(40, i, t(i)); s=0; forstep(i=2, 40, 3, s+=v[i]; print1(s", "))
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CROSSREFS
| Cf. A004188.
Sequence in context: A094159 A138976 A064043 * A027334 A130505 A027289
Adjacent sequences: A085786 A085787 A085788 * A085790 A085791 A085792
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Jon Perry (perry(AT)globalnet.co.uk), Jul 23 2003
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EXTENSIONS
| More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 18 2004
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