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A254963
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a(n) = n*(11*n + 3)/2.
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15
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0, 7, 25, 54, 94, 145, 207, 280, 364, 459, 565, 682, 810, 949, 1099, 1260, 1432, 1615, 1809, 2014, 2230, 2457, 2695, 2944, 3204, 3475, 3757, 4050, 4354, 4669, 4995, 5332, 5680, 6039, 6409, 6790, 7182, 7585, 7999, 8424, 8860, 9307, 9765, 10234, 10714, 11205
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OFFSET
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0,2
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COMMENTS
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This sequence provides the first differences of A254407 and the partial sums of A017473.
Also:
a(n) + n = n*(11*n+5)/2: 0, 8, 27, 57, 98, 150, 213, 287, ...;
a(n) + 2*n = n*(11*n+7)/2: 0, 9, 29, 60, 102, 155, 219, 294, ...;
a(n) - 3*n = n*(11*n-3)/2: 0, 4, 19, 45, 82, 130, 189, 259, ...;
a(n) + 5*n = n*(11*n+13)/2: 0, 12, 35, 69, 114, 170, 237, 315, ...;
a(n) + 6*n = n*(11*n+15)/2: 0, 13, 37, 72, 118, 175, 243, 322, ...;
a(n) + 7*n = n*(11*n+17)/2: 0, 14, 39, 75, 122, 180, 249, 329, ...;
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LINKS
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FORMULA
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G.f.: x*(7 + 4*x)/(1 - x)^3.
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MATHEMATICA
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Table[n (11 n + 3)/2, {n, 0, 50}]
LinearRecurrence[{3, -3, 1}, {0, 7, 25}, 50] (* Harvey P. Dale, Mar 25 2018 *)
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PROG
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(PARI) vector(50, n, n--; n*(11*n+3)/2)
(Sage) [n*(11*n+3)/2 for n in (0..50)]
(Magma) [n*(11*n+3)/2: n in [0..50]];
(Maxima) makelist(n*(11*n+3)/2, n, 0, 50);
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CROSSREFS
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Cf. similar sequences of the type 4*n^2 + k*n*(n+1)/2: A055999 (k=-7, n>6), A028552 (k=-6, n>2), A095794 (k=-5, n>1), A046092 (k=-4, n>0), A000566 (k=-3), A049450 (k=-2), A022264 (k=-1), A016742 (k=0), A022267 (k=1), A202803 (k=2), this sequence (k=3), A033580 (k=4).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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