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A084175
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Jacobsthal oblongs.
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9
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0, 1, 3, 15, 55, 231, 903, 3655, 14535, 58311, 232903, 932295, 3727815, 14913991, 59650503, 238612935, 954429895, 3817763271, 15270965703, 61084037575, 244335800775, 977343902151, 3909374210503, 15637499638215, 62549992960455
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n)=A001045(n)*A001045(n+1). Inverse binomial transform is A001019 doubled up. Binomial transform is A084177. Partial sums of A003683.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..500
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FORMULA
| a(n)=(2*4^n-(-2)^n-1)/9; a(n)=3*a(n-1)+6*a(n-2)-8*a(n-3), a(0)=0, a(1)=1, a(2)=3.
G.f.:x/((1+2*x)*(1-x)*(1-4*x)).
E.g.f.: (2*exp(4*x)-exp(x)-exp(-2*x))/9.
a(n+1)-4a(n)= 1, -1, 3, -5, 11, ... = A001045(n+1) signed. - Paul Curtz (bpcrtz(AT)free.fr), May 19 2008
a(n) = round(2^n/3) * round(2^(n+1)/3) [From Gary Detlefs (gdetlefs(AT)aol.com), Feb 10 2010]
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MAPLE
| for n from 1 to 25 do print(round(2^n/3)*round(2^(n+1)/3)) od; [From Gary Detlefs (gdetlefs(AT)aol.com), Feb 10 2010]
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MATHEMATICA
| Join[{a=0, b=1}, Table[c=2*b+8*a+1; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Feb 05 2011*)
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PROG
| (Sage) [gaussian_binomial(n, 2, -2) for n in xrange(1, 26)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
(MAGMA) [(2*4^n-(-2)^n-1)/9: n in [0..30]]; // Vincenzo Librandi, Jun 04 2011
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CROSSREFS
| Except for initial terms, same as A015249 and A084152.
Cf. A001654, A084158, A084159, A084152, A015249.
Sequence in context: A007973 A015249 A084152 * A081951 A033853 A049187
Adjacent sequences: A084172 A084173 A084174 * A084176 A084177 A084178
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 18 2003
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