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A105163
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a(n) = (n^3 - 7*n + 12)/6.
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11
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1, 1, 3, 8, 17, 31, 51, 78, 113, 157, 211, 276, 353, 443, 547, 666, 801, 953, 1123, 1312, 1521, 1751, 2003, 2278, 2577, 2901, 3251, 3628, 4033, 4467, 4931, 5426, 5953, 6513, 7107, 7736, 8401, 9103, 9843, 10622, 11441, 12301, 13203, 14148, 15137, 16171
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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A floretion-generated sequence relating to the sequence "A class of Boolean functions of n variables and rank 2" (among several others- see link "Sequences in Context").
a(n) = A181971(n,3) for n > 2. - Reinhard Zumkeller, Jul 09 2012
a(n) is the number of P-position in 2-modular Nim with n-1 piles. - Tanya Khovanova and Karan Sarkar, Jan 10 2016
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LINKS
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Michael De Vlieger, Table of n, a(n) for n = 1..10000
M. Janjic, Hessenberg Matrices and Integer Sequences, J. Int. Seq. 13 (2010), Article #10.7.8.
Nurul Hilda Syani Putri, Mashadi, and Sri Gemawati, Sequences from heptagonal pyramid corners of integer, International Mathematical Forum, Vol. 13, 2018, no. 4, 193-200.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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a(n) = A005581(n) + 1.
a(n) = C(n+1,n-2) - n + 2. - Zerinvary Lajos, Mar 21 2008
Sequence starting (1, 3, 8, 17, ...) = binomial transform of [1, 2, 3, 1, 0, 0, 0, ...]. - Gary W. Adamson, Apr 24 2008
G.f.: x*(1 - 3*x + 5*x^2 - 2*x^3)/(1 - x)^4. - Colin Barker, Mar 26 2012
a(n) = 2*a(n-1) - a(n-2) + n - 1, for all n in Z. - Gionata Neri, Jul 28 2016
a(n) = A000292(n-2) + A000124(n-2). - Torlach Rush, Aug 06 2018
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MAPLE
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seq(binomial(n+1, n-2)-n+2, n=1..44); # Zerinvary Lajos, Mar 21 2008
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MATHEMATICA
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Rest@ CoefficientList[Series[x (1 - 3 x + 5 x^2 - 2 x^3)/(1 - x)^4, {x, 0, 46}], x] (* or *)
Array[(#^3 - 7 # + 12)/6 &, 46] (* Michael De Vlieger, Nov 18 2019 *)
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PROG
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Floretion Algebra Multiplication Program, FAMP Code: 2jescycrokseq[ - .25'i - .25i' - .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' - .25e] RokType: Y[15] = Y[15] + p, X[15] = X[15] + 1 (internal program code)
(PARI) a(n)=(n^3-7*n)/6+2 \\ Charles R Greathouse IV, Mar 26 2012
(Maxima) A105163(n):=(n^3 - 7*n + 12)/6$ makelist(A105163(n), n, 1, 20); /* Martin Ettl, Dec 18 2012 */
(Python) for n in range(1, 45): print((n**3 - 7*n + 12)/6, end=', ') # Stefano Spezia, Jan 05 2019
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CROSSREFS
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Cf. A005581, A102169.
Sequence in context: A011889 A188426 A349975 * A011850 A141422 A076980
Adjacent sequences: A105160 A105161 A105162 * A105164 A105165 A105166
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KEYWORD
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nonn,easy
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AUTHOR
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Creighton Dement, Apr 10 2005
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STATUS
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approved
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