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A132925
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2^n - 1 + n*(n-1)/2.
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3
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1, 4, 10, 21, 41, 78, 148, 283, 547, 1068, 2102, 4161, 8269, 16474, 32872, 65655, 131207, 262296, 524458, 1048765, 2097361, 4194534, 8388860, 16777491, 33554731, 67109188, 134218078, 268435833, 536871317, 1073742258, 2147484112
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Row sums of triangle A132924. n-th Mersenne number + (n-1)-th triangular number.
Partial sums of A006127 [Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Oct 16 2009]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index to sequences with linear recurrences with constant coefficients, signature (5,-9,7,-2).
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FORMULA
| Binomial transform of [1, 3, 3, 2, 2, 2, 2,...].
a(n) = A000225(n) + A000217(n-1). [Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Oct 16 2009]
a(1)=1, a(2)=4, a(3)=10, a(4)=21, a(n)=5*a(n-1)-9*a(n-2)+ 7*a(n-3)- 2*a(n-4) [From Harvey P. Dale, June 19 2011]
G.f.: -x*(x^2+x-1)/((x-1)^3*(2*x-1)) [From Harvey P. Dale, June 19 2011]
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EXAMPLE
| a(4) = 21 = sum of row 4 terms of triangle A132924: (4 + 4 + 5 + 8).
a(4) = 21 = (1, 3, 3, 1) dot (1, 3, 3, 2) = (1 + 9 + 9 + 2).
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MAPLE
| A132925 := proc(n) 2^n-1+n*(n-1)/2 ; end proc; [R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 23 2009]
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MATHEMATICA
| Table[2^n-1+n (n-1)/2, {n, 40}] (* or *) LinearRecurrence[{5, -9, 7, -2}, {1, 4, 10, 21}, 40] (* From Harvey P. Dale, June 19 2011 *)
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PROG
| (PARI) a(n)=2^n+binomial(n, 2)-1 \ Charles R Greathouse IV, Jun 20 2011
(MAGMA) [2^n - 1 + n*(n-1)/2: n in [1..40]]; // Vincenzo Librandi, Jun 21 2011
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CROSSREFS
| Cf. A132924.
Sequence in context: A144897 A001891 A121497 * A053643 A111927 A109885
Adjacent sequences: A132922 A132923 A132924 * A132926 A132927 A132928
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KEYWORD
| nonn,easy
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 05 2007
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