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A081267
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Diagonal of triangular spiral in A051682.
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2
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1, 9, 26, 52, 87, 131, 184, 246, 317, 397, 486, 584, 691, 807, 932, 1066, 1209, 1361, 1522, 1692, 1871, 2059, 2256, 2462, 2677, 2901, 3134, 3376, 3627, 3887, 4156, 4434, 4721, 5017, 5322, 5636, 5959, 6291, 6632, 6982, 7341, 7709, 8086, 8472, 8867, 9271
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Milan Janjic, Two Enumerative Functions
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FORMULA
| a(n) = C(n, 0) + 8C(n, 1) + 9C(n, 2); binomial transform of (1, 8, 9, 0, 0, 0, .....). a(n) = (9n^2 + 7n + 2)/2. G.f.(1 + 6x + 2x^2)/(1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), for n>2. a(n) = right term in M^n * [1 1 1], where M = the 3X3 matrix [1 0 0 / 3 1 0 / 5 3 1]. M^n * [1 1 1] = [1 3n+1 a(n)]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 22 2004
a(n)=9*n+a(n-1)-1 (with a(0)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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EXAMPLE
| a(1)=9*1+1-1=9; a(2)=9*2+9-1=26; a(3)=9*3+26-1=52 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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CROSSREFS
| Cf. A081268.
Sequence in context: A022421 A075395 A085367 * A052153 A154560 A048468
Adjacent sequences: A081264 A081265 A081266 * A081268 A081269 A081270
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 15 2003
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