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A026039
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(d(n)-r(n))/5, where d = A026037 and r is the periodic sequence with fundamental period (1,2,0,2,0).
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2
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2, 4, 8, 13, 21, 31, 44, 61, 81, 106, 135, 169, 209, 254, 306, 364, 429, 502, 582, 671, 768, 874, 990, 1115, 1251, 1397, 1554, 1723, 1903, 2096, 2301, 2519, 2751, 2996, 3256, 3530, 3819, 4124, 4444, 4781, 5134, 5504, 5892, 6297, 6721, 7163, 7624, 8105, 8605, 9126, 9667, 10229, 10813, 11418, 12046, 12696, 13369
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,1
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 3..10000
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1,0,1,-3,3,-1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 24 2010]
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FORMULA
| a(n)=(n + 3)*(2*n^2 + 9*n + 22)/30 - 1/5 - ( - 1/25*((5 - 5^(1/2))^(1/2) - (5 + 5^(1/2))^(1/2))*2^(1/2))*sin(2*n*Pi/5) - (1/25*((5 - 5^(1/2))^(1/2) + (5 + 5^(1/2))^(1/2))*2^(1/2))*sin(4*n*Pi/5) [From Richard Choulet (richardchoulet(AT)yahoo.fr), Dec 14 2008]
a(n) = round((2*n-1)*(n^2-n+6)/30) = floor((2*n^3-3*n^2+13*n)/30) = ceil((n-1)*(2*n^2-n+12)/30) = round((n-1)*(2*n^2-n+12)/30) [From Mircea Merca (mircea(AT)teacher.com), Dec 03 2010]
a(n)= +3*a(n-1) -3*a(n-2) +a(n-3) +a(n-5) -3*a(n-6) +3*a(n-7) -a(n-8). G.f.: -x^3*(-2+2*x-2*x^2+x^3-2*x^4+3*x^5-3*x^6+x^7) / ( (x^4+x^3+x^2+x+1)*(x-1)^4 ) [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 24 2010]
a(n) = a(n-5)+n^2-6*n+13 , n>5 , a(1)=0, a(2)=1 [From Mircea Merca (mircea(AT)teacher.com), Dec 03 2010]
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MATHEMATICA
| f[n_] := Round[(2 n - 1)*(n^2 - n + 6)/30]; Array[f, 57, 3]
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PROG
| (MAGMA) [Round((2*n-1)*(n^2-n+6)/30): n in [3..60]]; /7 Vincenzo Librandi, Jun 25 2011
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CROSSREFS
| Sequence in context: A061866 A130840 A115266 * A004978 A005282 A046185
Adjacent sequences: A026036 A026037 A026038 * A026040 A026041 A026042
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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