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Search: id:A147874
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| 0, 3, 16, 39, 72, 115, 168, 231, 304, 387, 480, 583, 696, 819, 952, 1095, 1248, 1411, 1584, 1767, 1960, 2163, 2376, 2599, 2832, 3075, 3328, 3591, 3864, 4147, 4440, 4743, 5056, 5379, 5712, 6055, 6408, 6771, 7144, 7527, 7920, 8323, 8736, 9159, 9592, 10035
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Zero followed by partial sums of A017305.
Appears to be related to various other sequences: a(n) = A036666(2*n-2) for n>1; a(n) = A115006(2*n-3) for n>1; a(n) = A118015(5*n-6) for n>1; a(n) = A008738(5*n-7) for n>1.
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FORMULA
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a(n) = Sum_{k=0..n-2} 10*k+3 = Sum_{k=0..n-2} A017305(k). G.f.: (3*x+7*x^2)/(1-x)^3. a(n)=10*(n-2)+3+a(n-1). a(n)= 3*a(n-1)-3*a(n-2)+a(n-3).
a(n)=10*n+a(n-1)-17 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]
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EXAMPLE
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For n=2, a(2)=10*2+0-17=3; n=3, a(3)=10*3+3-17=16: n=4, a(4)=10*4+16-17=39 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]
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MATHEMATICA
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s=0; lst={s}; Do[s+=n++ +3; AppendTo[lst, s], {n, 0, 6!, 10}]; lst
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PROGRAM
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(MAGMA) [ 0 ] cat [ &+[ 10*k+3: k in [0..n-1] ]: n in [1..45] ]; [From Klaus Brockhaus, Nov 17 2008]
(MAGMA) [ 5*n^2-2*n: n in [0..45] ];
(PARI) {m=45; a=7; for(n=0, m, print1(a=a+10*(n-1)+3, ", "))} [From Klaus Brockhaus, Nov 17 2008]
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CROSSREFS
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Cf. A017305 (10n+3), A036666, A115006, A118015 (Floor(n^2/5)), A008738 (Floor((n^2+1)/5)).
Sequence in context: A068415 A066875 A081270 this_sequence A092466 A152618 A004320
Adjacent sequences: A147871 A147872 A147873 this_sequence A147875 A147876 A147877
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KEYWORD
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nonn
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008
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EXTENSIONS
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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 17 2008, Nov 20 2008
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