A063522
a(n) = n*(5*n^2 - 3)/2.
Original entry on oeis.org
0, 1, 17, 63, 154, 305, 531, 847, 1268, 1809, 2485, 3311, 4302, 5473, 6839, 8415, 10216, 12257, 14553, 17119, 19970, 23121, 26587, 30383, 34524, 39025, 43901, 49167, 54838, 60929, 67455, 74431, 81872, 89793, 98209, 107135, 116586, 126577, 137123, 148239, 159940
Offset: 0
- Harry J. Smith, Table of n, a(n) for n = 0..1000
- T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (11).
- Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).
(1/12)*t*(n^3 - n) + n for t = 2, 4, 6, ... gives
A004006,
A006527,
A006003,
A005900,
A004068,
A000578,
A004126,
A000447,
A004188,
A004466,
A004467,
A007588,
A062025,
A063521,
A063522,
A063523.
-
[n*(5*n^2 -3)/2: n in [0..30]]; // G. C. Greubel, May 02 2018
-
lst={};Do[AppendTo[lst, LegendreP[3, n]], {n, 10^2}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 11 2008 *)
CoefficientList[Series[x*(1 + 13*x + x^2)/(1-x)^4, {x, 0, 50}], x] (* G. C. Greubel, Sep 01 2017 *)
LinearRecurrence[{4,-6,4,-1},{0,1,17,63},40] (* Harvey P. Dale, Sep 06 2023 *)
-
a(n) = { n*(5*n^2 - 3)/2 } \\ Harry J. Smith, Aug 25 2009
A335333
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of 1/sqrt(1 - 2*(2*k+1)*x + x^2).
Original entry on oeis.org
1, 1, 1, 1, 3, 1, 1, 5, 13, 1, 1, 7, 37, 63, 1, 1, 9, 73, 305, 321, 1, 1, 11, 121, 847, 2641, 1683, 1, 1, 13, 181, 1809, 10321, 23525, 8989, 1, 1, 15, 253, 3311, 28401, 129367, 213445, 48639, 1, 1, 17, 337, 5473, 63601, 458649, 1651609, 1961825, 265729, 1
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 3, 5, 7, 9, 11, ...
1, 13, 37, 73, 121, 181, ...
1, 63, 305, 847, 1809, 3311, ...
1, 321, 2641, 10321, 28401, 63601, ...
1, 1683, 23525, 129367, 458649, 1256651, ...
-
T[n_, k_] := LegendreP[n, 2*k + 1]; Table[T[k, n - k], {n, 0, 9}, {k, 0, n}] // Flatten (* Amiram Eldar, May 03 2021 *)
-
T(n, k) = pollegendre(n, 2*k+1);
A160751
a(n) is the smallest n-digit prime formed by appending a digit to a(n-1); a(1)=6.
Original entry on oeis.org
6, 61, 613, 6131
Offset: 1
-
A160751 := proc(n) option remember ; local d; if n =1 then 6; else for d from 1 to 9 by 2 do if isprime(10*procname(n-1)+d) then RETURN( 10*procname(n-1)+d ) ; fi; od: RETURN(-1) ; fi; end: seq(A160751(n),n=1..10) ; # R. J. Mathar, May 26 2009
Showing 1-3 of 3 results.
Comments