Original entry on oeis.org
0, 7, 120, 1921, 30624, 488071, 7778520, 123968257, 1975713600, 31487449351, 501823476024, 7997688167041, 127461187196640, 2031381306979207, 32374639724470680, 515962854284551681, 8223031028828356224
Offset: 0
John C. Hallyburton, Jr. (hallyb(AT)vmsdev.enet.dec.com)
- G. C. Greubel, Table of n, a(n) for n = 0..825
- K. R. S. Sastry, Problem 533 The College Mathematics Journal, 25, issue 4, 1994, p. 334.
- K. R. S. Sastry, Square Products of Sums of Squares The College Mathematics Journal, 26, issue 4, 1995, p. 333.
- Index entries for linear recurrences with constant coefficients, signature (17,-17,1).
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a:=[0,7,120];; for n in [4..30] do a[n]:=17*a[n-1]-17*a[n-2]+a[n-3]; od; a; # G. C. Greubel, Feb 10 2020
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I:=[0,7,120]; [n le 3 select I[n] else 17*Self(n-1) -17*Self(n-2) +Self(n-3): n in [1..30]]; // G. C. Greubel, Feb 10 2020
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seq(simplify((4*ChebyshevU(n,8) -11*ChebyshevU(n-1,8) -4)/7)), n = 0..30); # G. C. Greubel, Feb 10 2020
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Table[(4*ChebyshevU[n,8] -11*ChebyshevU[n-1,8] -4)/7, {n,0,30}] (* G. C. Greubel, Feb 10 2020 *)
LinearRecurrence[{17,-17,1},{0,7,120},20] (* Harvey P. Dale, Dec 01 2022 *)
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a(n)=local(w); w=8+3*quadgen(28); imag(w^n)+4*(real(w^n)-1)/7
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vector(31, n, my(m=n-1); (4*polchebyshev(m,2,8) -11*polchebyshev(m-1,2,8) -4)/7 ) \\ G. C. Greubel, Feb 10 2020
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[(4*chebyshev_U(n,8) -11*chebyshev_U(n-1,8) -4)/7 for n in (0..30)] # G. C. Greubel, Feb 10 2020
Original entry on oeis.org
1, 24, 391, 6240, 99457, 1585080, 25261831, 402604224, 6416405761, 102259887960, 1629741801607, 25973608937760, 413948001202561, 6597194410303224, 105141162563649031, 1675661406608081280
Offset: 1
John C. Hallyburton, Jr. (hallyb(AT)vmsdev.enet.dec.com)
- Mentioned in a problem on p. 334 of Two-Year College Math. Jnl., Vol. 25, 1994.
- G. C. Greubel, Table of n, a(n) for n = 1..825
- K. R. S. Sastry, Problem 533 The College Mathematics Journal, 25, issue 4, 1994, p. 334.
- K. R. S. Sastry, Square Products of Sums of Squares The College Mathematics Journal, 26, issue 4, 1995, p. 333.
- Index entries for linear recurrences with constant coefficients, signature (17,-17,-1).
-
a:=[1,24,391];; for n in [4..30] do a[n]:=17*a[n-1]-17*a[n-2]+a[n-3]; od; a; # G. C. Greubel, Mar 04 2020
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I:=[1,24,391]; [n le 3 select I[n] else 17*Self(n-1) -17*Self(n-2) +Self(n-3): n in [1..30]]; // G. C. Greubel, Mar 04 2020
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seq( simplify( (4*ChebyshevU(n,8) - 53*ChebyshevU(n-1,8) -4)/7), n=1..20); # G. C. Greubel, Mar 04 2020
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Table[(4*ChebyshevU[n, 8] -53*ChebyshevU[n-1, 8] -4)/7, {n,20}] (* G. C. Greubel, Mar 04 2020 *)
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a(n)=local(w); w=8+3*quadgen(28); imag(1/w^n)+4*(real(1/w^n)-1)/7
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vector(30, n, (4*polchebyshev(n,2,8) -53*polchebyshev(n-1,2,8) -4)/7 ) \\ G. C. Greubel, Mar 04 2020
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[(4*chebyshev_U(n,8) -53*chebyshev_U(n-1,8) -4)/7 for n in (1..30)] # G. C. Greubel, Mar 04 2020
A073352
Positive integers making n^2*(n-1)*(2*n-1)^2*(7*n-1)/36 a square.
Original entry on oeis.org
1, 4, 55, 868, 13825, 220324, 3511351, 55961284, 891869185, 14213945668, 226531261495, 3610286238244, 57538048550401, 916998490568164, 14614437800540215, 232914006318075268, 3712009663288664065
Offset: 0
G.f. = 1 + 4*x + 55*x^2 + 868*x^3 + 13825*x^4 + 220324*x^5 + 3511351*x^6 + ...
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a:=[1,4,55];; for n in [4..30] do a[n]:=17*a[n-1]-17*a[n-2]+a[n-3]; od; a; # G. C. Greubel, Feb 09 2020
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I:=[1,4,55]; [n le 3 select I[n] else 17*Self(n-1) - 17*Self(n-2) + Self(n-3): n in [1..30]]; // G. C. Greubel, Feb 09 2020
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seq( simplify((4 +3*ChebyshevU(n,8) -24*ChebyshevU(n-1,8))/7), n=0..30); # G. C. Greubel, Feb 09 2020
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LinearRecurrence[{17,-17,1},{1,4,55},30] (* Harvey P. Dale, Dec 09 2018 *)
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{a(n) = if( n<0, a(-n), if( n<1, 1, 16*a(n-1) - a(n-2) - 8))}
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{a(n) = (4 + 3 * real((8 + 3 * quadgen(28))^n)) / 7}
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[(4 +3*chebyshev_U(n,8) -24*chebyshev_U(n-1,8))/7 for n in (0..30)] # G. C. Greubel, Feb 09 2020
A073351
n^2(n+1)(2n+1)^2(7n+1)/36.
Original entry on oeis.org
0, 4, 125, 1078, 5220, 18150, 50869, 122500, 263568, 519840, 956725, 1664234, 2762500, 4407858, 6799485, 10186600, 14876224, 21241500, 29730573, 40876030, 55304900, 73749214, 97057125, 126204588, 162307600, 206635000, 260621829
Offset: 0
- Mentioned in a problem on p. 334 of Two-Year College Math. Jnl., Vol. 25, 1994.
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