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A062708 Write 0,1,2,3,4,... in a triangular spiral; then a(n) is the sequence found by reading the terms along the line from 0 in the direction 0,2,... 9
0, 2, 13, 33, 62, 100, 147, 203, 268, 342, 425, 517, 618, 728, 847, 975, 1112, 1258, 1413, 1577, 1750, 1932, 2123, 2323, 2532, 2750, 2977, 3213, 3458, 3712, 3975, 4247, 4528, 4818, 5117, 5425, 5742, 6068, 6403, 6747, 7100, 7462, 7833, 8213, 8602, 9000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = n*(9*n-5)/2.
a(n) = 9*n + a(n-1) - 7 (with a(0)=0). - Vincenzo Librandi, Aug 07 2010
From Colin Barker, Jul 07 2012: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(2+7*x)/(1-x)^3. (End)
a(n) = A218470(9n+1). - Philippe Deléham, Mar 27 2013
E.g.f.: x*(4 + 9*x)*exp(x)/2. - G. C. Greubel, Sep 02 2019
EXAMPLE
The spiral begins:
.
15
/ \
16 14
/ \
17 3 13
/ / \ \
18 4 2 12
/ / \ \
19 5 0---1 11
/ / \
20 6---7---8---9--10
.
From Vincenzo Librandi, Aug 07 2010: (Start)
a(1) = 9*1 + 0 - 7 = 2;
a(2) = 9*2 + 2 - 7 = 13;
a(3) = 9*3 + 13 - 7 = 33. (End)
MAPLE
seq(n*(9*n-5)/2, n=0..50); # G. C. Greubel, Sep 02 2019
MATHEMATICA
Table[n*(9*n-5)/2, {n, 0, 50}] (* G. C. Greubel, Sep 02 2019 *)
nxt[{n_, a_}]:={n+1, 9(n+1)+a-7}; NestList[nxt, {0, 0}, 50][[All, 2]] (* Harvey P. Dale, Apr 11 2022 *)
PROG
(PARI) a(n)=n*(9*n-5)/2 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [n*(9*n-5)/2: n in [0..50]]; // G. C. Greubel, Sep 02 2019
(Sage) [n*(9*n-5)/2 for n in (0..50)] # G. C. Greubel, Sep 02 2019
(GAP) List([0..50], n-> n*(9*n-5)/2); # G. C. Greubel, Sep 02 2019
CROSSREFS
Cf. A051682.
Cf. A218470.
Cf. numbers of the form n*(n*k-k+4))/2 listed in A226488 (this is case k=9).
Sequence in context: A084828 A100512 A051474 * A296293 A190816 A084910
KEYWORD
nonn,easy
AUTHOR
Floor van Lamoen, Jul 21 2001
STATUS
approved

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Last modified April 15 11:42 EDT 2024. Contains 371681 sequences. (Running on oeis4.)