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A195309 Row sums of an irregular triangle read by rows in which row n lists the next A026741(n+1) natural numbers A000027. 2
1, 9, 11, 45, 39, 126, 94, 270, 185, 495, 321, 819, 511, 1260, 764, 1836, 1089, 2565, 1495, 3465, 1991, 4554, 2586, 5850, 3289, 7371, 4109, 9135, 5055, 11160, 6136, 13464, 7361, 16065, 8739, 18981, 10279, 22230, 11990, 25830, 13881 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The integers in same rows of the source triangle have a property related to Euler's Pentagonal Theorem.
Note that the column 1 of the mentioned triangle gives the positive terms of A001318 (see example).
LINKS
FORMULA
a(n) = (n+1)*(9*n^2+18*n-1+(3*n^2+6*n+1)*(-1)^n)/32 . - R. J. Mathar, Oct 08 2011
G.f. x*(1+9*x+7*x^2+9*x^3+x^4) / ( (x-1)^4*(1+x)^4 ). - R. J. Mathar, Oct 08 2011
EXAMPLE
a(1) = 1
a(2) = 2+3+4 = 9
a(3) = 5+6 = 11
a(4) = 7+8+9+10+11 = 45
a(5) = 12+13+14 = 39
a(6) = 15+16+17+18+19+20+21 = 126
a(7) = 22+23+24+25 = 94
a(8) = 26+27+28+29+30+31+32+33+34 = 270
a(9) = 35+36+37+38+39 = 185
MAPLE
A195309 := proc(n)
(n+1)*(9*n^2+18*n-1+(3*n^2+6*n+1)*(-1)^n)/32
end proc:
seq(A195309(n), n=1..60) ; # R. J. Mathar, Oct 08 2011
MATHEMATICA
LinearRecurrence[{0, 4, 0, -6, 0, 4, 0, -1}, {1, 9, 11, 45, 39, 126, 94, 270}, 80] (* Harvey P. Dale, Jun 22 2015 *)
CROSSREFS
Cf. A026741, A195310, A195311, A004188 (bisection).
Sequence in context: A345109 A143465 A201999 * A242507 A116152 A215831
KEYWORD
nonn
AUTHOR
Omar E. Pol, Sep 21 2011
STATUS
approved

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Last modified March 28 14:13 EDT 2024. Contains 371254 sequences. (Running on oeis4.)