A029885
Boustrophedon transform of 1 followed by Thue-Morse sequence A001285.
Original entry on oeis.org
1, 2, 5, 13, 34, 108, 415, 1841, 9381, 53733, 342086, 2395481, 18300250, 151453434, 1349856656, 12890177378, 131298281746, 1420980348324, 16283235530691, 196958363484995, 2507751773736087, 33526171616091612
Offset: 0
- Reinhard Zumkeller, Table of n, a(n) for n = 0..400
- Peter Luschny, An old operation on sequences: the Seidel transform.
- J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory, 17A (1996) 44-54 (Abstract, pdf, ps).
- N. J. A. Sloane, Transforms.
- Wikipedia, Boustrophedon transform.
- Index entries for sequences related to boustrophedon transform
-
a029885 n = sum $ zipWith (*) (a109449_row n) (1 : map fromIntegral a001285_list)
-- Reinhard Zumkeller, Nov 04 2013
-
tm[n_] := Mod[Sum[Mod[Binomial[n, k], 2], {k, 0, n}], 3];
T[n_, k_] := (n!/k!) SeriesCoefficient[(1 + Sin[x])/Cos[x], {x, 0, n - k}];
a[n_] := Sum[T[n, k] If[k == 0, 1, tm[k - 1]], {k, 0, n}];
Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Jul 02 2019 *)
A230951
Boustrophedon transform of Thue-Morse sequence A010059.
Original entry on oeis.org
1, 1, 1, 3, 9, 27, 108, 475, 2421, 13859, 88254, 617957, 4720980, 39070669, 348225424, 3325303894, 33871280413, 366573108019, 4200618576106, 50809739256049, 646929695900154, 8648812936664311, 121132117170628444, 1773647319453218254, 27099334868109293640
Offset: 0
- Reinhard Zumkeller, Table of n, a(n) for n = 0..400
- Peter Luschny, An old operation on sequences: the Seidel transform
- J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory, 17A 44-54 1996 (Abstract, pdf, ps).
- Wikipedia, Boustrophedon transform
- Index entries for sequences related to boustrophedon transform
-
a230951 n = sum $ zipWith (*) (a109449_row n) $ map fromIntegral a010059_list
-
from itertools import count, islice, accumulate
def A230951_gen(): # generator of terms
blist = tuple()
for i in count(0):
yield (blist := tuple(accumulate(reversed(blist), initial=i.bit_count()&1^1)))[-1]
A230951_list = list(islice(A230951_gen(),30)) # Chai Wah Wu, Apr 17 2023
A230952
Boustrophedon transform of Hamming weight (A000120).
Original entry on oeis.org
0, 1, 3, 8, 23, 72, 280, 1242, 6331, 36236, 230726, 1615584, 12342422, 102145644, 910393530, 8693609421, 88552405435, 958361506524, 10982014291650, 132835979792636, 1691320230842116, 22611285878526978, 316685416851528722, 4636988553066906265
Offset: 0
- Reinhard Zumkeller, Table of n, a(n) for n = 0..400
- Peter Luschny, An old operation on sequences: the Seidel transform
- J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory, 17A 44-54 1996 (Abstract, pdf, ps).
- Wikipedia, Boustrophedon transform
- Index entries for sequences related to boustrophedon transform
-
a230952 n = sum $ zipWith (*) (a109449_row n) $ map fromIntegral a000120_list
(Python 3.10+)
from itertools import accumulate, count, islice
def A230952_gen(): # generator of terms
blist = tuple()
for i in count(0):
yield (blist := tuple(accumulate(reversed(blist),initial=i.bit_count())))[-1]
A230952_list = list(islice(A230952_gen(),40)) # Chai Wah Wu, Jun 12 2022
-
T[n_, k_] := (n!/k!) SeriesCoefficient[(1 + Sin[x])/Cos[x], {x, 0, n - k}];
a[n_] := Sum[T[n, k] DigitCount[k, 2, 1], {k, 0, n}];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Jul 23 2019 *)
A230958
Boustrophedon transform of Thue-Morse sequence A001285.
Original entry on oeis.org
1, 3, 7, 15, 39, 127, 480, 2143, 10907, 62495, 397814, 2785861, 21282228, 176133285, 1569817724, 14990658724, 152693582275, 1652531857935, 18936620009722, 229053108410969, 2916394751599614, 38989325834726043, 546070266163669664, 7995699956778626764
Offset: 0
- Reinhard Zumkeller, Table of n, a(n) for n = 0..400
- Peter Luschny, An old operation on sequences: the Seidel transform.
- J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory Ser. A, 76(1) (1996), 44-54 (Abstract, pdf, ps).
- J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory Ser. A, 76(1) (1996), 44-54.
- Ludwig Seidel, Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [USA access only through the HATHI TRUST Digital Library]
- Ludwig Seidel, Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [Access through ZOBODAT]
- Wikipedia, Boustrophedon transform.
- Index entries for sequences related to boustrophedon transform
-
a230958 n = sum $ zipWith (*) (a109449_row n) $ map fromIntegral a001285_list
-
T[n_, k_] := (n!/k!) SeriesCoefficient[(1 + Sin[x])/Cos[x], {x, 0, n - k}];
tm[n_] := Mod[Sum[Mod[Binomial[n, k], 2], {k, 0, n}], 3];
Table[Sum[T[n, k] tm[k], {k, 0, n}], {n, 0, 23}] (* Jean-François Alcover, Jul 23 2019 *)
-
from itertools import accumulate, count, islice
def A230958_gen(): # generator of terms
blist = tuple()
for i in count(0):
yield (blist := tuple(accumulate(reversed(blist), initial=2 if i.bit_count()&1 else 1)))[-1]
A230958_list = list(islice(A230958_gen(),30)) # Chai Wah Wu, Apr 17 2023
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